Accurate calculation of high order pseudo-Zernike moments and their numerical stability |
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| Affiliation: | 1. Department of Computer Science, Punjabi University, Patiala 147002, India;2. Department of Mathematics, Sri Guru Granth Sahib World University, Fatehgarh Sahib, India;1. Institute for Frontier Medical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8507, Japan;2. Graduate School of Engineering, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan;1. German Space Operations Center (GSOC), Deutsches Zentrum für Luft-und Raumfahrt (DLR), Münchener Straße 20, D-82234 Weßling, Germany;2. Institut für Astronomische und Physikalische Geodäsie, Technische Universität München, Arcisstraße 21, D-80290 München, Germany;1. State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, PR China;2. University of Chinese Academy of Sciences, Beijing 100049, PR China;3. Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, PR China;1. State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, PR China;2. University of Chinese Academy of Sciences, Beijing 100049, PR China;3. Xiamen University, Xiamen 361005, PR China |
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| Abstract: | The accuracy of pseudo-Zernike moments (PZMs) suffers from various errors, such as the geometric error, numerical integration error, and discretization error. Moreover, the high order moments are vulnerable to numerical instability. In this paper, we present a method for the accurate calculation of PZMs which not only removes the geometric error and numerical integration error, but also provides numerical stability to PZMs of high orders. The geometric error is removed by taking the square-grids and arc-grids, the ensembles of which maps exactly the circular domain of PZMs calculation. The Gaussian numerical integration is used to eliminate the numerical integration error. The recursive methods for the calculation of pseudo-Zernike polynomials not only reduce the computation complexity, but also provide numerical stability to high order moments. A simple computational framework to implement the proposed approach is also discussed. Detailed experimental results are presented which prove the accuracy and numerical stability of PZMs. |
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| Keywords: | Pseudo-Zernike moments Invariance property Orthogonal moments Accurate moments |
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